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The angular speed on a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in rad/s2 is :
- a)4π
- b)12π
- c)104π
- d)2π
Correct answer is option 'A'. Can you explain this answer?
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To find the angular acceleration in rad/s^2, we need to convert the angular speeds from rpm to rad/s and use the formula for angular acceleration.
Given:
Initial angular speed, ω1 = 1200 rpm
Final angular speed, ω2 = 3120 rpm
Time, t = 16 seconds
1 revolution = 2π radians
1 minute = 60 seconds
Converting initial angular speed to rad/s:
ω1 = 1200 rpm * (2π radians/1 revolution) * (1 minute/60 seconds)
=> ω1 = 1200 * 2π / 60 rad/s
=> ω1 = 40π rad/s
Converting final angular speed to rad/s:
ω2 = 3120 rpm * (2π radians/1 revolution) * (1 minute/60 seconds)
=> ω2 = 3120 * 2π / 60 rad/s
=> ω2 = 104π rad/s
Using the formula for angular acceleration:
ω2 = ω1 + αt, where α is the angular acceleration
104π = 40π + α * 16
64π = 16α
Dividing both sides by 16:
4π = α
The angular acceleration in rad/s^2 is 4π.
Given:
Initial angular speed, ω1 = 1200 rpm
Final angular speed, ω2 = 3120 rpm
Time, t = 16 seconds
1 revolution = 2π radians
1 minute = 60 seconds
Converting initial angular speed to rad/s:
ω1 = 1200 rpm * (2π radians/1 revolution) * (1 minute/60 seconds)
=> ω1 = 1200 * 2π / 60 rad/s
=> ω1 = 40π rad/s
Converting final angular speed to rad/s:
ω2 = 3120 rpm * (2π radians/1 revolution) * (1 minute/60 seconds)
=> ω2 = 3120 * 2π / 60 rad/s
=> ω2 = 104π rad/s
Using the formula for angular acceleration:
ω2 = ω1 + αt, where α is the angular acceleration
104π = 40π + α * 16
64π = 16α
Dividing both sides by 16:
4π = α
The angular acceleration in rad/s^2 is 4π.
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The angular speed on a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in rad/s2 is :a)4πb)12πc)104πd)2πCorrect answer is option 'A'. Can you explain this answer?
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